Phonons in twisted bilayer graphene

Abstract

We theoretically investigated phonon dispersion in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. The calculations were performed using the Born-von-Karman model for the intra-layer atomic interactions and the Lennard-Jones potential for the inter-layer interactions. It was found that the stacking order affects the outof-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA-or AB-stacked bilayer graphene appears in the phonon frequencies range 90 -110 cm -1 . Twisting bilayer graphene leads to emergence of new phonon branchestermed entangled phononswhich originate from mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the entangled phonon depend strongly on the rotation angle and can be used for non-contact identification of the twist angles in graphene samples. The obtained results and tabulated frequencies of phonons in twisted bilayer graphene are important for interpretation of experimental Raman data and determining thermal conductivity of these materials systems.

Specific heat of twisted bilayer graphene: Engineering phonons by atomic plane rotations

“…Recently the attention has been shifted to twisted few-layer graphene (T-FLG), which demonstrates intriguing electron [24][25][26][27] and phonon properties [28][29][30][31][32][33][34][35][36]. Several independent experimental Raman studies of twisted graphene found series of phonon peaks in different energy regions, which are absent in FLG without the twist [28][29][30][32][33][34][35][36][37].…”

“…It was found that the rotational angle strongly influences ZO phonon modes. We have theoretically investigated the hybrid folded phonons in twisted bilayer graphene using the Born-von Karman model for the intralayer interactions and Lennard-Jones potential for the interlayer interactions [32]. We have shown that the twist angle affects the low-energy phonons the most while the phonon 3 density of states (PDOS) and phonon average group velocity depend only weakly on the rotational angle [32].…”

“…While the electronic properties of T-FLG were extensively investigated theoretically [26][27] the theoretical studies of phonons in T-FLG are rare [31][32]. In one reported study the Brenner potential for the intralayer interaction and Lennard-Jones potential for the interlayer interactions have been used to investigate phonon modes in a circular twisted bilayer graphene (T-BLG) with a finite radius R = 0.5 nm -3 nm [31].…”

“…Here  is the phonon frequency, [19,32,39]. Therefore, a proper choice of the force constant matrices  is crucial for obtaining the correct phonon frequencies and for accurate calculation of phonon specific heat.…”

“…We have theoretically investigated the hybrid folded phonons in twisted bilayer graphene using the Born-von Karman model for the intralayer interactions and Lennard-Jones potential for the interlayer interactions [32]. We have shown that the twist angle affects the low-energy phonons the most while the phonon 3 density of states (PDOS) and phonon average group velocity depend only weakly on the rotational angle [32]. While the thirst theoretical studies of the phonon spectra in T-FLG appeared there have been no reported investigations of thermal properties such as specific heat or thermal conductivity.…”